Bias toward the null hypothesis in model-free linkage analysis is highly dependent on the test statistic used

Recently, it has been suggested that traditional nonparametric multipoint-linkage procedures can show a "bias" toward the null hypothesis of no effect when there is incomplete information about allele sharing at genotyped marker loci (or at positions in between marker loci). Here, I investigate the extent of this bias for a variety of test statistics commonly used in qualitative- ("affecteds only") and quantitative-trait linkage analysis. Through simulation and analytical derivation, I show that many of the test statistics available in standard linkage analysis packages (such as Genehunter, Merlin, and Allegro) are, in fact, not affected by this bias problem. A few test statistics--most notably the nonparametric linkage statistic and, to a lesser extent, the Aspex-MLS and Haseman-Elston statistics--are affected by the bias. Variance-components procedures, although unbiased, can show inflation or deflation of the test statistic attributable to the inclusion of pairs with incomplete identity-by-descent information. Results obtained--for instance, in genome scans--using these methods might therefore be worth revisiting to see if greater power can be obtained by use of an alternative statistic or by eliminating or downweighting uninformative relative pairs.     

HLA and genomewide allele sharing in dizygotic twins

Gametic selection during fertilization or the effects of specific genotypes on the viability of embryos may cause a skewed transmission of chromosomes to surviving offspring. A recent analysis of transmission distortion in humans reported significant excess sharing among full siblings. Dizygotic (DZ) twin pairs are a special case of the simultaneous survival of two genotypes, and there have been reports of DZ pairs with excess allele sharing around the HLA locus, a candidate locus for embryo survival. We performed an allele-sharing study of 1,592 DZ twin pairs from two independent Australian cohorts, of which 1,561 pairs were informative for linkage on chromosome 6. We also analyzed allele sharing in 336 DZ twin pairs from The Netherlands. We found no evidence of excess allele sharing, either at the HLA locus or in the rest of the genome. In contrast, we found evidence of a small but significant (P=.003 for the Australian sample) genomewide deficit in the proportion of two alleles shared identical by descent among DZ twin pairs. We reconciled conflicting evidence in the literature for excess genomewide allele sharing by performing a simulation study that shows how undetected genotyping errors can lead to an apparent deficit or excess of allele sharing among sibling pairs, dependent on whether parental genotypes are known. Our results imply that gene-mapping studies based on affected sibling pairs that include DZ pairs will not suffer from false-positive results due to loci involved in embryo survival.     

Transmission-ratio distortion and allele sharing in affected sib pairs: a new linkage statistic with reduced bias, with application to chromosome 6q25.3

We studied the effect of transmission-ratio distortion (TRD) on tests of linkage based on allele sharing in affected sib pairs. We developed and implemented a discrete-trait allele-sharing test statistic, Sad, analogous to the Spairs test statistic of Whittemore and Halpern, that evaluates an excess sharing of alleles at autosomal loci in pairs of affected siblings, as well as a lack of sharing in phenotypically discordant relative pairs, where available. Under the null hypothesis of no linkage, nuclear families with at least two affected siblings and one unaffected sibling have a contribution to Sad that is unbiased, with respect to the effects of TRD independent of the disease under study. If more distantly related unaffected individuals are studied, the bias of Sad is generally reduced compared with that of Spairs, but not completely. Moreover, Sad has higher power, in some circumstances, because of the availability of unaffected relatives, who are ignored in affected-only analyses. We discuss situations in which it may be an efficient use of resources to genotype unaffected relatives, which would give insights for promising study designs. The method is applied to a sample of pedigrees ascertained for asthma in a chromosomal region in which TRD has been reported. Results are consistent with the presence of transmission distortion in that region.     

The significance of not finding a gene

As more investigators conduct extensive whole-genome linkage scans for complex traits, interest is growing in meta-analysis as a way of integrating the weak or conflicting evidence from multiple studies. However, there is a bias in the most commonly used meta-analysis linkage technique (i.e., Fisher's [1925] method of combining of P values) when it is applied to many nonparametric (i.e., model free) linkage results. The bias arises in those methods (e.g., variance components, affected sib pair, extremely discordant sib pairs, etc.) that truncate all "negative evidence against linkage" into the single value of LOD = 0. If incorrectly handled, this bias can artificially inflate or deflate the combined meta-analysis linkage results for any given locus. This is an especially troublesome problem in the context of a genome scan, since LOD = 0 is expected to occur over half the unlinked genome. The bias can be overcome (nearly) completely by simply interpreting LOD = 0 as a P value of 1divided by 2ln(2) is approximately equal to .72 in Fisher's formula.     

A genome-wide search for genes predisposing to familial psoriasis by using a stratification approach

We have performed a genome scan, using markers spaced by 10 cM, in the search for psoriasis-susceptibility loci. The family material of 134 affected sibling pairs was ascertained on the basis of a population genetic study in which 65% of the probands had two healthy parents. Genotyping results were analyzed for non-random excessive allele-sharing between sib pairs by using GENEHUNTER ver 1.1. A stratification approach was applied to increase the homogeneity of the material by means of an operational definition of joint complaints among affected individuals. Significant linkage to the human leukocyte antigen region on chromosome 6p in a cohort including 42 families without joint complaints (nonparametric linkage score of 2.83, P=0.002) strongly supported the validity of this operational definition as it replicated results from an earlier linkage report with similar stratification criteria. New candidate regions on chromosomes 3 and 15 were identified. The highest non-parametric linkage values in this study, 2.96 (P=0.0017) and 2.89 (P=0.0020), were reached on chromosome 15 in a subgroup with joint complaints and on chromosome 3 in a subgroup without joint complaints. In addition, confirmation of previously reported loci was established on chromosomes 4q, 6p, and 17q. This study indicates that distinct disease loci might be involved in psoriasis etiology for various phenotypes.     

Effects of stratification in the analysis of affected-sib-pair data: benefits and costs

The benefits and costs of stratification of affected-sib-pair (ASP) data were examined in three situations: (1) when there is no difference in identity-by-descent (IBD) allele sharing between stratified and unstratified ASP data sets; (2) when there is an increase in IBD allele sharing in one of the stratified groups; and (3) when the data are stratified on the basis of IBD allele-sharing status at one locus, and the stratified ASPs are then analyzed for linkage at a second locus. When there is no difference in IBD sharing between strata, a penalty is always paid for stratifying the data. The loss of power to detect linkage in the stratified ASP data sets is the result of multiple testing and the smaller sample size within individual strata. In the case in which etiologic heterogeneity (i.e., severity of phenotype, age at onset) represents genetic heterogeneity, the power to detect linkage can be increased by stratifying the ASP data. This benefit is obtained when there is sufficient IBD allele sharing and sample sizes. Once linkage has been established for a given locus, data can be stratified on the basis of IBD status at this locus and can be tested for linkage at a second locus. When the relative risk is in the vicinity of 1, the power to detect linkage at the second locus is always greater for the unstratified ASP data set. Even for values of the relative risk that diverge sufficiently from 1, with adequate sample sizes and IBD allele sharing, the benefits of stratifying ASP data are minimal.     

The affected-/discordant-sib-pair design can guarantee validity of multipoint model-free linkage analysis of incomplete pedigrees when there is marker-marker disequilibrium

Genomewide linkage studies are tending toward the use of single-nucleotide polymorphisms (SNPs) as the markers of choice. However, linkage disequilibrium (LD) between tightly linked SNPs violates the fundamental assumption of linkage equilibrium (LE) between markers that underlies most multipoint calculation algorithms currently available, and this leads to inflated affected-relative-pair allele-sharing statistics when founders' multilocus genotypes are unknown. In this study, we investigate the impact that the degree of LD, marker allele frequency, and association type have on estimating the probabilities of sharing alleles identical by descent in multipoint calculations and hence on type I error rates of different sib-pair linkage approaches that assume LE. We show that marker-marker LD does not inflate type I error rates of affected sib pair (ASP) statistics in the whole parameter space, and that, in any case, discordant sib pairs (DSPs) can be used to control for marker-marker LD in ASPs. We advocate the ASP/DSP design with appropriate sib-pair statistics that test the difference in allele sharing between ASPs and DSPs.     

A putative susceptibility locus on chromosome 18 is not a major contributor to human selective IgA deficiency: evidence from meiotic mapping of 83 multiple-case families.

Previous reports of an association between constitutional chromosome 18 abnormalities and low levels of IgA suggested that this chromosome contains a susceptibility locus for selective IgA deficiency (IgAD), the most frequent Ig deficiency in humans. IgAD is genetically related to common variable immunodeficiency (CVID), characterized by a lack of additional isotypes. Our previous linkage analysis of 83 multiple-case IgAD/CVID families containing 449 informative pedigree members showed a significantly increased allele sharing in the chromosome region 6p21 consistent with allelic associations in family-based and case-control studies and provided the evidence for a predisposing locus, termed IGAD1, in the proximal part of the MHC. We have typed the same family material at 17 chromosome 18 marker loci with the average intermarker distance of 7 cM. A total of 7633 genotypes were analyzed in a nonparametric linkage analysis, but none of the marker loci exhibited a significantly increased allele sharing in affected family members. In addition, reverse painting and deletion mapping of a panel of constitutional chromosome 18 deletions/translocations showed the presence of IgA-deficient and IgA-proficient patients with the same abnormality and did not reveal a region commonly deleted. The linkage analysis of chromosome 8 and 21 regions involved in reciprocal translocations t(8;18) and t(18;21), which were identified in two patients lacking IgA, did not disclose a significant allele sharing. Although these results do not exclude the presence of a minor predisposing locus on this chromosome, such a putative locus would confer a population risk of developing IgAD/CVID much lower than IGAD1.     

Isolation and characterization of 150 novel microsatellite markers for Zhikong scallop (Chlamys farreri)

We isolated and characterized 150 novel microsatellite markers of Zhikong scallop (Chlamys farreri) from three simple sequence repeat‐enriched libraries constructed with (GA)₁₅ and (CA)₁₅. The polymorphism was assessed with 48 individuals, and the result showed the number of allele ranged from two to 30, with an average of 8.4 alleles/locus. The values of observed and expected heterozygosities ranged from 0.0791 to 0.9878 and from 0 to 1.0000, respectively. Sixty‐five loci showed significant departure from Hardy–Weinberg equilibrium, and 14 locus pairs displayed linkage disequilibrium. These markers are therefore potentially useful for conservation studies, population structure assessment, ecological analyses and linkage map construction.     

Matrix representation of the Haseman-Elston method.

The Hasemann-Elston method of linkage detection is based on the probabilities of a sib pair having 0, 1, or 2 alleles identical by descent (IBD) at a marker and a trait locus. These probabilities form a 3x3 matrix. Here, the characteristic values and characteristic vectors of this matrix were used to clarify the structure of the equations and to simplify calculations. As examples, the regression coefficients were derived for three genetic systems: a trait and a marker, two epistatic traits and two markers, and one trait locus and two markers. The last model was studied under the assumption of no crossover interference, the expression for allele IBD sharing at a trait locus was derived as a function of allele IBD sharing at two marker loci, and the regression is shown to be non-linear.     

Linkage of Bipolar Affective Disorder to Chromosome 18 Markers in a New Pedigree Series

Several groups have reported evidence suggesting linkage of bipolar affective disorder (BPAD) to chromosome 18. We have reported data from 28 pedigrees that showed linkage to marker loci on 18p and to loci 40 cM distant on 18q. Most of the linkage evidence derived from families with affected phenotypes in only the paternal lineage and from marker alleles transmitted on the paternal chromosome. We now report results from a series of 30 new pedigrees (259 individuals) genotyped for 13 polymorphic markers spanning chromosome 18. Subjects were interviewed by a psychiatrist and were diagnosed by highly reliable methods. Genotypes were generated with automated technology and were scored blind to phenotype. Affected sib pairs showed excess allele sharing at the 18q markers D18S541 and D18S38. A parent-of-origin effect was observed, but it was not consistently paternal. No robust evidence of linkage was detected for markers elsewhere on chromosome 18. Multipoint nonparametric linkage analysis in the new sample combined with the original sample of families supports linkage on chromosome 18q, but the susceptibility gene is not well localized.     

Mapping genes underlying ethnic differences in disease risk by linkage disequilibrium in recently admixed populations.

Where recent admixture has occurred between two populations that have different disease rates for genetic reasons, family-based association studies can be used to map the genes underlying these differences, if the ancestry of the alleles at each locus examined can be assigned to one of the two founding populations. This article explores the statistical power and design requirements of this approach. Markers suitable for assigning the ancestry of genomic regions could be defined by grouping alleles at closely spaced microsatellite loci into haplotypes, or generated by representational difference analysis. For a given relative risk between populations, the sample size required to detect a disease locus that accounts for this relative risk by linkage-disequilibrium mapping in an admixed population is not critically dependent on assumptions about genotype penetrances or allele frequencies. Using the transmission-disequilibrium test to search the genome for a locus that accounts for a relative risk of between 2 and 3 in a high-risk population, compared with a low-risk population, generally requires between 150 and 800 case-parent pairs of mixed descent. The optimal strategy is to conduct an initial study using markers spaced at < or = 10 cM with cases from the second and third generations of mixed descent, and then to map the disease loci more accurately in a subsequent study of a population with a longer history of admixture. This approach has greater statistical power than allele-sharing designs and has obvious applications to the genetics of hypertension, non-insulin-dependent diabetes, and obesity.     

Using overall allele-sharing to detect the presence of large-scale data errors and parameter misspecification in sib-pair linkage studies

Data errors and marker allele frequency misspecification can lead to incorrect inference in linkage analysis. Here we demonstrate the effect of each on an allele-sharing statistic in a sample of sib pairs. In the context of relationship testing, we propose a new test that compares the sample genome-wide sib-pair allele sharing to its expectation and show that this test can detect the presence of large-scale data and model errors.     

Extensive genomic conservation of cattle microsatellite heterozygosity in sheep

We report the evaluation of 1036 bovine microsatellite primer pairs for their suitability as linkage markers in sheep. Approximately 58% (605/1036) of bovine primer pairs amplified a locus in sheep. Sixty-seven per cent (409/605) of amplified loci were detected as polymorphic. Marker heterozygosity, allele number and range of allele sizes were significantly lower in sheep than cattle sampled in this study. However, median fragment size was similar. These data suggest that high-resolution comparative linkage maps between closely related species can be constructed relatively efficiently.     

Comparison of Haseman-Elston regression analyses using single, summary, and longitudinal measures of systolic blood pressure

To compare different strategies for linkage analyses of longitudinal quantitative trait measures, we applied the "revisited" Haseman-Elston (RHE) regression model (the cross product of centered sib-pair trait values is regressed on expected identical-by-descent allele sharing) to cross-sectional, summary, and repeated measurements of systolic blood pressure (SBP) values in replicate 34, randomly selected from the Genetic Analysis Workshop 13 simulated data. RHE linkage scans were performed without knowledge of the generating model using the following phenotypes derived from untreated SBP measurements: the first, the last, the mean, the ratio of the change between the first and last over time, and the estimated linear regression slope coefficient. Estimates of allele sharing in sibling pairs were obtained from the complete genotype data of Cohorts 1 and 2, but linkage analyses were restricted to the five visits of Cohort 2 siblings. Evidence for linkage was suggestive (p < 0.001) at markers neighboring SBP genes Gb35, Gs10, and Gs12, but weaker signals (p < 0.01) were obtained at markers mapping close to Gb34 and Gs11. Linkage to baseline genes Gb34 and Gb35 was best detected using the first SBP measurement, whereas linkage to slope genes Gs10-12 was best detected using the last or mean SBP value. At markers on chromosomes 13 and 21 displaying strongest linkage signals, marginal RHE-type models including repeated SBP measures were fit to test for overall and time-dependent genetic effects. These analyses assumed independent sib pairs and employed generalized estimating equations (GEE) with a first-order autoregressive working correlation structure to adjust for serial correlation present among repeated observations from the same sibling pair.     

Affected-sib-pair analyses reveal support of prior evidence for a susceptibility locus for bipolar disorder, on 21q.

In 22 multiplex pedigrees screened for linkage to bipolar disorder, by use of 18 markers on chromosome 21q, single-locus affected-sib-pair (ASP) analysis detected a high proportion (57%-62%) of alleles shared identical by descent (IBD), with P values of .049-.0008 on nine marker loci. Multilocus ASP analyses revealed locus trios in the distal region between D21S270 and D21S171, with excess allele sharing (nominal P values <.01) under two affection-status models, ASM I (bipolars and schizoaffectives) and ASM II (ASM I plus recurrent unipolars). In addition, under ASM I, the proximal interval spanned by D21S1436 and D21S65 showed locus trios with excess allele sharing (nominal P values of .03-.0003). These findings support prior evidence that a susceptibility locus for bipolar disorder is on 21q.     

How to model a complex trait. 1. General considerations and suggestions

Usually, when complex traits are at issue, not only are the loci of the responsible genes a priori unknown; the same also holds for the mode of inheritance of the trait, and sometimes even for the phenotype definition. The term mode of inheritance relates to both the genetic mechanism, i.e., the number of loci implicated in the etiology of the disease, and the genotype-phenotype relation, which describes the influence of these loci on the trait. Having an idea of the genetic model can crucially facilitate the mapping process. This holds especially in the context of linkage analysis, where an appropriate parametric model or a suitable nonparametric allele sharing statistic may accordingly be selected. Here, we review the difficulties with parametric and nonparametric linkage analysis when applied to multifactorial diseases. We address the question why it is necessary to adequately model a genetically complex trait in a linkage study, and elucidate the steps to do so. Furthermore, we discuss the value of including unaffected individuals into the analysis, as well as of looking at larger pedigrees, both with parametric and nonparametric methods. Our considerations and suggestions aim at guiding researchers to genotyping individuals at a trait locus as accurately as possible.     

Evidence for Linkage of Bipolar Disorder to Chromosome 18 with a Parent-of-Origin Effect

A susceptibility gene on chromosome 18 and a parent-of-origin effect have been suggested for bipolar affective disorder (BPAD). We have studied 28 nuclear families selected for apparent unilineal transmission of the BPAD phenotype, by using 31 polymorphic markers spanning chromosome 18. Evidence for linkage was tested with affected-sib-pair and LOD score methods under two definitions of the affected phenotype. The affected-sib-pair analyses indicated excess allele sharing for markers on 18p within the region reported previously. The greatest sharing was at D18S37: 64% in bipolar and recurrent unipolar (RUP) sib pairs (P = .0006). In addition, excess sharing of the paternally, but not maternally, transmitted alleles was observed at three markers on 18q: at D18S41, 51 bipolar and RUP sib pairs were concordant for paternally transmitted alleles, and 21 pairs were discordant (P = .0004). The evidence for linkage to loci on both 18p and 18q was strongest in the 11 paternal pedigrees, i.e., those in which the father or one of the father's sibs is affected. In these pedigrees, the greatest allele sharing (81%; P = .00002) and the highest LOD score (3.51; θ = 0.0) were observed at D18S41. Our results provide further support for linkage of BPAD to chromosome 18 and the first molecular evidence for a parent-of-origin effect operating in this disorder. The number of loci involved, and their precise location, require further study.     

Characterization of 30 new microsatellite markers,developed from enriched genomic DNA library of zoysiagrass Zoysia japonica Steud.

The present study reports the development of 30 polymorphic microsatellite markers for zoysiagrass Zoysia japonica Steud. The 30 markers produced a total of 125 alleles with an average of 4.2 alleles per locus. Values for observed and expected heterozygosities ranged from 0.10 to 0.95 and from 0.15 to 0.81, respectively. At significance threshold (P < 0.05), 11 loci deviated from Hardy–Weinberg equilibrium, whereas significant linkage disequilibrium values were observed between 16 pairs of loci. These markers may provide information needed to select genetically diverse parents for developing breeding and mapping populations of zoysiagrass.     

Linkage of interleukin 6 locus to human osteopenia by sibling pair analysis

Osteopenia and osteoporosis are common human conditions considered to result from the interplay of multiple genetic and environmental factors. Twin and family studies have yielded strong correlations between levels of bone mass and a number of genetic factors. The genes involved could regulate metabolism, formation and resorption of bone, all processes that determine bone mass. We tested 192 sibling pairs of adult Japanese women from 136 families for genetic linkage between osteopenia and allelic variants of four candidate genes (interleukin-6, interleukin-6 receptor, calcium-sensing receptor, and matrix gla protein) using qualitative and quantitative methods, and using as genetic markers dinucleotide-repeat polymorphisms present in or near each of those loci. The interleukin-6 locus showed evidence of linkage to osteopenia analyzed as a qualitative trait, with mean allele sharing of 0.40 (P=0.0001) in discordant pairs and 0.55 (P=0.04) in concordant affected pairs. Variation at this locus was also linked to decreased bone mineral density measured as a quantitative trait (P=0.02). Analyses limited only to the post-menopausal women showed similar or even stronger results. No other locus among those tested showed any evidence of linkage by either method. The results provided strong evidence that genetic variation at the interleukin-6 locus affects regulation of bone mineral metabolism and confers risk for osteopenia and osteoporosis in adult women.